Ratios of moments of baryon distributions

These lattice measurements were presented in the paper "Lattice
QCD predictions for shapes of event distributions along the freezeout
curve in heavy-ion collisions" by R.V. Gavai and Sourendu Gupta
[arXiv:1001.3796]. Please
cite this paper if you use these measurements.

The ratio m3

√SNN(GeV)

z = μB/T

Tc=160 MeV

Tc=165 MeV

Tc=170 MeV

Tc=175 MeV

Tc=180 MeV

Tc=185 MeV

Tc=190 MeV

11.5

2.08 ± 0.07

0.94 ± 0.015.41 1.2 ± 0.6

0.92 ± 0.015.40 -5 ± 2

0.89 ± 0.015.390± 1

0.86 ± 0.01NANA

0.84 ± 0.01NANA

0.82 ± 0.01NANA

0.80 ± 0.01NANA

18.0

1.39 ± 0.05

1.00 ± 0.015.42 2.7 ± 4

0.97 ± 0.015.4151.2 ± 0.5

0.94 ± 0.015.41 -1± 2

0.91 ± 0.015.40 46±33

0.89 ± 0.015.39 0± 1

0.86 ± 0.01NANA

0.84 ± 0.01NANA

19.6

1.29 ± 0.04

1.00 ± 0.015.42 2.8 ± 0.3

0.97 ± 0.015.4151.4 ± 0.6

0.94 ± 0.015.41 -0.2± 0.6

0.91 ± 0.015.40 -0.12±0.01

0.89 ± 0.015.39 0.1 ± 1.3

0.86 ± 0.01NANA

0.84 ± 0.01NANA

27.0

0.96 ± 0.02

1.02 ± 0.015.43 0 ± 2

0.99 ± 0.015.42 2.8 ± 0.3

0.96 ± 0.015.415-3± 5

0.93 ± 0.015.41 0.7±0.5

0.91 ± 0.015.40 16± 5

0.88 ± 0.015.39 -1± 2

0.86 ± 0.01NANA

39.0

0.68 ± 0.02

1.03 ± 0.015.43 0.8 ± 0.7

1.00 ± 0.015.42 3.0 ± 0.2

0.97 ± 0.015.4151.1± 0.4

0.94 ± 0.015.41 0±1

0.92 ± 0.015.40 5.7± 0.8

0.89 ± 0.015.39 -47± 39

0.87 ± 0.01NANA

62.4

0.44 ± 0.02

1.03 ± 0.015.431.8 ± 0.1

1.00 ± 0.015.423.36 ± 0.09

0.97 ± 0.015.4152.6 ± 0.5

0.94 ± 0.015.412.6 ± 0.3

0.92 ± 0.015.404.5 ± 0.3

0.89 ± 0.015.396.8 ± 0.4

0.87 ± 0.015.396.8 ± 0.4

200.0

0.142 ± 0.005

1.04 ± 0.015.436.94 ± 0.03

1.01 ± 0.015.436.94 ± 0.03

0.98 ± 0.015.427.43 ± 0.02

0.95 ± 0.015.417.16 ± 0.08

0.92 ± 0.015.407.69 ± 0.06

0.90 ± 0.015.397.89 ± 0.09

0.88 ± 0.015.397.89 ± 0.09

For each √SNN and Tc, the first line is the value of T/Tc,
the second, the lattice parameter β which corresponds to a run at
the nearest T/Tc, and the third (in bold), the value of m3.
There are no runs corresponding to the fields marked NA.

For the lattice determination one uses the relation m3(z,T/Tc)=χ(4)(z,T/Tc)/χ(3)(z,T/Tc).
This should equal the combination which can be determined in experiment: m3=Kσ/S, where K is the Kurtosis, σ the
square root of the variance and S the skewness.

The ratios m1,2,3

Tc=170 MeV

√SNN(GeV)

z = μB/T

β

m1

m2

m3

11.5

2.08 ± 0.07

5.39

2 ± 1

1.85 ± 0.03

0 ± 1

18.0

1.39 ± 0.05

5.41

1.5 ± 0.5

-0.3 ± 0.6

-1±2

19.6

1.29 ± 0.04

5.41

1.4 ± 0.4

-0.7 ± 0.7

-0.2±0.6

27.0

0.96 ± 0.02

5.415

3 ± 2

-1.2 ± 0.3

-3 ± 5

39.0

0.68 ± 0.02

5.415

0.58 ± 0.05

1.17 ± 0.1

1.1±0.4

62.4

0.44 ± 0.02

5.415

0.52 ± 0.03

1.6 ± 0.5

2.6 ± 0.5

200.0

0.142 ± 0.005

5.42

0.146 ± 0.005

0.92 ± 0.03

7.43 ± 0.02

For each √SNN the values of z and the lattice parameter β (corresponding
to Tc=170 MeV) are listed along with the values of >m1, m2
and m3. There are no runs corresponding to the fields marked NA. These were the
values used in the figures.

Tc=175 MeV

√SNN(GeV)

z = μB/T

β

m1

m2

m3

11.5

2.08 ± 0.07

NA

NA

NA

NA

18.0

1.39 ± 0.05

5.40

0.9 ± 0.8

-1.4 ± 0.3

46±33

19.6

1.29 ± 0.04

5.40

1.1 ± 0.7

-1.4 ± 0.3

10.12±12

27.0

0.96 ± 0.02

5.41

0.9 ± 0.2

1.4 ± 0.5

0.7±0.5

39.0

0.68 ± 0.02

5.41

0.6 ± 0.1

1.7 ± 0.4

6±2

62.4

0.44 ± 0.02

5.41

0.4 ± 0.1

1.2 ± 0.2

2.9 ± 0.3

200.0

0.142 ± 0.005

5.41

0.14 ± 0.02

1.0 ± 0.1

7.16 ± 0.08

For each √SNN the values of z and the lattice parameter β (corresponding
to Tc=175 MeV) are listed along with the values of >m1, m2
and m3.
There are no runs corresponding to the fields marked NA.